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通过一种不同的数值方法研究非线性分数阶微分问题非负解的存在性。

The existence of nonnegative solutions for a nonlinear fractional -differential problem via a different numerical approach.

作者信息

Samei Mohammad Esmael, Ahmadi Ahmad, Hajiseyedazizi Sayyedeh Narges, Mishra Shashi Kant, Ram Bhagwat

机构信息

Department of Mathematics, Bu-Ali Sina University, Hamedan, 65178 Iran.

Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.

出版信息

J Inequal Appl. 2021;2021(1):75. doi: 10.1186/s13660-021-02612-z. Epub 2021 Apr 23.

DOI:10.1186/s13660-021-02612-z
PMID:33907360
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8063195/
Abstract

This paper deals with the existence of nonnegative solutions for a class of boundary value problems of fractional -differential equation with three-point conditions for on a time scale , where , , and , based on the Leray-Schauder nonlinear alternative and Guo-Krasnoselskii theorem. Moreover, we discuss the existence of nonnegative solutions. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

摘要

本文基于Leray-Schauder非线性抉择定理和郭-克拉斯诺谢尔斯基定理，研究了时间尺度(\mathbb{T})上一类具有三点条件的分数阶微分方程边值问题非负解的存在性，其中(\alpha\in(0,1))，(p\in(1,+\infty))，且(q\in(1,+\infty))。此外，我们还讨论了非负解的存在性。给出了涉及算法和示例图的例子，以证明我们理论结果的有效性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/b77867ccc594/13660_2021_2612_Fig6_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/7a4ea1cbc930/13660_2021_2612_Figc_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/281079f60196/13660_2021_2612_Fige_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/33d887289402/13660_2021_2612_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/f1d5644b3119/13660_2021_2612_Fig2_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/dc51be181da1/13660_2021_2612_Figh_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/b77867ccc594/13660_2021_2612_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/e5ea02e7a60f/13660_2021_2612_Figa_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/25821fe53b77/13660_2021_2612_Figb_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/7a4ea1cbc930/13660_2021_2612_Figc_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/cb0455a1020a/13660_2021_2612_Figd_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/281079f60196/13660_2021_2612_Fige_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/33d887289402/13660_2021_2612_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/f1d5644b3119/13660_2021_2612_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/e3514510d0fe/13660_2021_2612_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/478d5fe646f9/13660_2021_2612_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/fe69a318e38d/13660_2021_2612_Figf_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/51c0a187d993/13660_2021_2612_Figg_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/471bcc2a0855/13660_2021_2612_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/dc51be181da1/13660_2021_2612_Figh_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5283/8063195/b77867ccc594/13660_2021_2612_Fig6_HTML.jpg

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